People didn't love Napoleon III much but they were OK with having him around. Until Sedan. A lot of French coin collections probably hit the junk pile after that.
These coins are the most common of the 10 centime issues, and continued in circulation until 1935. Since they were cheap, people in the 1920's and 1930's probably tried to form sets of what they could find in circulation, like Americans collect Lincoln cents and
Jefferson nickels. They're hefty and substantial compared to the little nickel Lindauer 10 C's that replaced them, so more desirable. It would be like large cents circulating side-by-side with small cents. Worn out large cents...high grade Napoleon III's are pretty scarce and get premium prices.
I hunt for the comparative rarities in this series. In the US no one seems to know or care that several of the 1857's are relatively more valuable than the others. But these coins were not scarce - mintages are all over a million. I suspect they are like lower mintage Lincolns and Indian Heads: the hardest holes to fill to complete the series.
I used to pick the French books of a dealer who had close to a full set. I bought everything that was VF or higher, as well as the 1857's. I made several buying trips over 3-4 years and it never looked like anything had been purchased between trips. Compared to French catalog prices the coins were ridiculously cheap. But considering that there were no other buyers it's not surprising.